Question

a. Convert 3% simple monthly rate into simple annual rate. b. Convert 6% simple annual rate into annual rate, compounded monthly. c. Convert 9% annual rate compounded monthly into annual rate, compounded daily. d. Convert 12% annual rate, compounded weekly into simple annual rate. e. Convert 24% simple annual rate to annual rate, compounded continuously. Show All Work.

Answer 1

(A)

3% simple monthly rate which is simple annual rate/12:-

Therefore, Simple annual rate = 3% *12 ; = 36% simple annual rate

(B)

given 6% simple annual rate. to convert into annual rate compounded monthly:-

= (1+0.06)^12

= 1.0616778

Now, = (1.0616778 -1)*100%

= 6.17%

(C) 9% compounded monthly. lets find the APR for the EAR 9% compounded monthly.

= 1.09^(1/12) ; = 1.0072073

Now, = 1.0072073 -1 ; = 0.0072073*100*12 ; = 8.648788%

Now converting this into the EAR for compounding daily assuming 365 days a years:-

= (1+0.08648788/365)^365

= 9.0326%

(D)

Assuming 52 weeks a year:-

= 1.12^(1/52) ; = 1.002181774

Now, = (1.002181774 -1)*100*52 ; = 11.34%

(E)

Using above equation:-

Rc = 1*ln(1+0.24/1) ; = 0.21511 or 21.511%